9x^2+21x+2=0

Solution for 9x^2+21x+2=0 equation:

9x^2+21x+2=0

a = 9; b = 21; c = +2;
Δ = b2-4ac
Δ = 212-4·9·2
Δ = 369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{41}}{2*9}=\frac{-21-3\sqrt{41}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{41}}{2*9}=\frac{-21+3\sqrt{41}}{18}
$